Lagrange multiplier is a technique to determine a local minima or maxima of an objective function subject to some constraint. It allow us to convert the given objective function and the constraint into a single objective function, which we can use with traditional techniques, like equating the derivative to zero, to determine a local minima or maxima.
The distribution of a random variable is quite detailed — it contains all the probabilistic information of the random variable. Analogous to the summaries of the sample data sets like mean and variance, we can define summaries of the probability distributions. This post presents various summaries or properties of probability distributions.
The notion of probability distribution of a random variable can be extended to the joint distribution of multiple random variables. On the same lines, we can define the joint pdf, joint cumulative distribution and other various definitions for multiple random variables.
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